AP EAMCET202120 Aug 2021Evening ShiftMathematicsStraight LinesActual
The points ( 2 , 3 , 4 ) , ( - 1 , - 2 , 1 ) and ( 5 , 8 , 7 ) are
Options
- Acollinear
- Bvertices of a right-angled triangle
- Cvertices of an equilateral triangle
- Dvertices of an isosceles triangle
Correct answer
A. collinear
Step-by-step solution
Let a line A C divides at B in ratio m : n A ( 2 , 3 , 4 ) , B - 1 , - 2 , 1   &   C 5 , 8 , 7 So ( - 1 , 2 , 1 ) = m x 2 + n x 1 m + n , m y 2 + n y 1 m + n , m z 2 + n z 1 m + n ⇒ - 1 , 2 , 1 = 5 m + 2 n m + n , 8 m + n m + n , 7 m + 4 n m + n ⇒ - 1 = 5 m + 2 n m + n , - 2 = 8 m + n m + n , 1 = 7 m + 4 n m + n ⇒ m n = - 1 2 , m n = - 1 2 , m n = - 1 2 Ratio are same. It means points are collinear.